Question

. An object whose mass is 375 lb falls freely under the influence of gravity from an initial elevation of 253 ft above the surface of Earth. The initial velocity is downward with a magnitude of 10 ft/s. The effect of air resistance is negligible. (a) Determine the speed, in ft/s, of the object just before it strikes the surface of Earth. (b) Calculate the kinetic energy of the object, in Btu, before it strikes the surface of Earth. Assume that the gravitational acceleration is g

Answer 1

(a) Vf = 128 ft/s

(b) K.E = 122.8 Btu

Step-by-step explanation:

(a)

In order to find the velocity of the object just before striking the surface of earth or the final velocity, we use 3rd equation of motion:

2gh = Vf² - Vi²

where,

g = 32.2 ft/s²

h = height = 253 ft

Vf = Final Velocity = ?

Vi = Initial Velocity = 10 ft/s

Therefore,

(2)(32.2 ft/s²)(253 ft) = Vf² - (10 ft/s)²

16293.2 ft²/s² + 100 ft²/s² = Vf²

Vf = √(16393.2 ft²/s²)

Vf = 128 ft/s

(b)

The kinetic energy of the object before it hits the surface of earth is given by:

K.E = (0.5)(m)(Vf)²

where,

m = mass of object = 375 lb

K.E = Kinetic energy of object before it strikes the surface of earth = ?

Therefore,

K.E = (0.5)(375 lb)(128 ft/s)²

K.E = 3073725 lb.ft²/s²

Now, converting this to Btu:

K.E = (3073725 lb.ft²/s²)(1 Btu/25037 lb.ft²/s²)

K.E = 122.8 Btu